Find the derivatives of the following from first principles (a) f(x) = 4x^2 (b) g(x) = VX +3 (c) y = f(x) + g(x)
Answers
The derivative of y = f(x) + g(x) is y' = 8x + 1 / (2√x).
(a) To find the derivative of the function f(x) = 4x^2 using first principles, we start by taking the limit as h approaches 0 of the difference quotient:
f'(x) = lim(h->0) [f(x + h) - f(x)] / h
Substituting f(x) = 4x^2 into the equation, we have:
f'(x) = lim(h->0) [(4(x + h)^2 - 4x^2) / h]
Expanding and simplifying the numerator:
f'(x) = lim(h->0) [(4(x^2 + 2xh + h^2) - 4x^2) / h]
= lim(h->0) [(4x^2 + 8xh + 4h^2 - 4x^2) / h]
= lim(h->0) (8x + 4h)
= 8x
Therefore, the derivative of f(x) = 4x^2 is f'(x) = 8x.
(b) To find the derivative of the function g(x) = √x + 3 using first principles, we again use the difference quotient:
g'(x) = lim(h->0) [g(x + h) - g(x)] / h
Substituting g(x) = √x + 3 into the equation:
g'(x) = lim(h->0) [√(x + h) + 3 - (√x + 3)] / h
= lim(h->0) [√(x + h) - √x] / h
To simplify the expression, we multiply the numerator and denominator by the conjugate of the numerator (√(x + h) + √x):
g'(x) = lim(h->0) [(√(x + h) - √x)(√(x + h) + √x)] / (h(√(x + h) + √x))
= lim(h->0) [(x + h) - x] / (h(√(x + h) + √x))
= lim(h->0) h / (h(√(x + h) + √x))
= lim(h->0) 1 / (√(x + h) + √x)
= 1 / (2√x)
Therefore, the derivative of g(x) = √x + 3 is g'(x) = 1 / (2√x).
(c) To find the derivative of y = f(x) + g(x), we can apply the sum rule of differentiation. Since we know the derivatives of f(x) and g(x) from parts (a) and (b) respectively, the derivative of y with respect to x is:
y' = f'(x) + g'(x)
= 8x + 1 / (2√x)
Hence, the derivative of y = f(x) + g(x) is y' = 8x + 1 / (2√x).
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Related Questions
bro I deaxvdaxvss put 100 points in this- someone help a struggling girl out
Answers
Answer:
6. P, y=5x
5. P, y=2x
4. N, N
Step-by-step explanation:
If the graph is a straight line that goes through (0, 0), then it represents a proportional relation. The constant in the proportion (k) can be read from the graph as the y-value that corresponds to x=1.
__
6. P, y = 5x
5. P, y = 2x
4. N, N . . . . The y-intercept is not zero, so this is not a proportional relation.
Determine if the two triangles shown are similar. If so, write the similarity statement.
A) Impossible to determine.
B) ATUS ABSC
C) ATUS-ABCS
D) The triangles are not similar.
Answers
Answer:
C) ATUS-ABCS
Step-by-step explanation:
ΔTUS ΔBSC would also be a right answer, but remember that the order of the points matter.
Both of these triangles share a point S, so the order of where the S is placed should be the same.
In this answer, ΔTUS ΔBCS, notice that the S is in the end of the triangle notation.
However, in this answer, ΔTUS ΔBSC, the S is in the end of ΔTUS while the S is in the middle of ΔBSC even S is the correspondent point for both triangles.
Hence, ΔTUS ΔBCS is the correct notation and correct answer.
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12. A population of carpenter ants is called a(n) _______ ___________________
Answers
Answer:
swarmers
Step-by-step explanation:
hope this helps
HELP ME ON THIS QUESTION
Answers
Answer:
168
Step-by-step explanation:
(11 +17) ×12 /2
28×12 /2
=168
all about formule
Answer:
C. 168ft²
Step-by-step explanation:
area: S = a + b /2 × h
S = 11 + 17 / 2 × 12
S = 28/2 × 12
S = 14 × 12
S = 168
Which choice is equivalent to the fraction below when x is an appropriate
value? Hint: Rationalize the denominator and simplify.
4-√6z
O A.
OB. 8+2√62
16-6z
O C.
8+2√/6z
8-3
D.
2+√6z
4-6z
8-6z
Answers
The correct option is D)\(2+\sqrt{6z} /4-6z\) .The choice is equivalent to the given fraction when x is an appropriate value is \(2+\sqrt{6z} /4-6z\)
Let's rationalize the denominator of the given fraction as shown below:
\($4 - \sqrt{6z} = \frac{(4 - \sqrt{6z}) (\overline{4 + \sqrt{6z}})}{(4 - \sqrt{6z}) (\overline{4 + \sqrt{6z}})}$\)
Here, the denominator is of the form\($(a-b)(a+b)$\), which can be written as \($a^2 - b^2$\).
Therefore, the above expression can be simplified as:
\(\[\frac{(4 - \sqrt{6z}) (\overline{4 + \sqrt{6z}})}{(4 - \sqrt{6z}) (\overline{4 + \sqrt{6z}})} \\= \frac{(4^2 - \sqrt{(6z)^2})}{(4 - \sqrt{6z}) (\overline{4 + \sqrt{6z}})}\\\\= \frac{16 - 6z}{16 - (6z)}\\\\= \frac{16 - 6z}{10} = \frac{8-3z}{5}\]\)
Therefore, we can see that choice D) \(2+\sqrt{6z} /4-6z\) is equivalent to the given fraction when x is an appropriate value.
Thus, the correct option is D) \(2+\sqrt{6z} /4-6z\)
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I know the answer is .78, but don’t understand why? .9-.6X.2
Answers
It may be confusing because the decimals aren’t like whole numbers.
Step-by-step explanation:
When you multiply 0.6 and 0.2, you do not get 1.2. Rather, the product would be 0.12.
We have the equation \(0.9-(0.6)(0.2)\)
To show you what is happening, lets convert these numbers into fractions
This would give us \(\frac{9}{10} -(\frac{6}{10})(\frac{2}{10})\)
Recall that when you multiply two fractions, you multiply the numerators and denominators separately. Doing so gives us
\(\frac{9}{10} -\frac{6*2}{10*10}\)
Which then becomes
\(\frac{9}{10} -\frac{12}{100}\)
The last thing we need to do is to create a common denominator
\(\frac{90}{100}-\frac{12}{100}=\frac{78}{100} =0.78\)
Another way to see what is happening is by thinking about the numbers in scientific notation. Doing so would give us
\(9*10^{-1}-(6*10^{-1})(2*10^{-1})\)
Once we multiply these terms, we get
\(9*10^{-1}-6*10^{-1}*2*10^{-1}\\\\9*10^{-1}-12*10^{-2}\)
Now we can convert these numbers into decimals to get
\(0.9-0.12=0.78\)
if DF=78, DE=5x-9, and EF=2x+10 Find EF
Answers
Answer:
EF = 32
Step-by-step explanation:
DE + EF = DF
5x - 9 + 2x + 10 = 78
5x + 2x + 10 - 9= 78
7x + 1 = 78
7x = 78 - 1
7x = 77
x = 77/7
x = 11
\(EF=2x+10 = 2 \times 11 + 10 \\ EF=22 + 10 \\ \huge \red { \boxed{EF=32}}\)
Find the appropriate critical value for constructing a confidence interval in the following setting. Estimating a population proportion p at a 94% confidence level based on an SRS of size 125.
Answers
The appropriate critical value for constructing a confidence interval in this setting is 1.88.
To find the appropriate critical value for constructing a confidence interval at a 94% confidence level, we can use a standard normal distribution table or a calculator.
First, we need to find the value of alpha, which is the significance level, which is equal to 1 - the confidence level. In this case, alpha is equal to 1 - 0.94 = 0.06.
Next, we need to find the critical value z* from the standard normal distribution table or calculator, which corresponds to the area to the right of z* being equal to alpha/2 = 0.03.
Using a standard normal distribution table or calculator, we can find that the critical value z* is approximately 1.88.
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When we are computing a simple linear regression line, there are certain conditions that must be met for this model to be valid. One of these conditions is the equal spread condition. Which of these answers best explains how we check to make sure that this condition is met? a. Make sure there is similar spread around the sample mean of x. b. Make sure there is similar spread around the line at each value of x.
c. Make sure that there is similar spread around the sample mean of y. d. Make sure all outliers are only below the line.
Answers
The answers that best explains how we check to make sure that this condition is met is: c. Make sure there is similar spread around the sample mean of y.
How we check to make sure that this condition is met?The equal spread condition states that the residuals (differences between the actual and predicted values of y) should have roughly equal variance at each value of x.
To check if this condition is met, we examine the residual plot, which is a scatterplot of the residuals versus the independent variable x. If the spread of residuals around the mean is roughly equal for all x, then the equal spread condition is satisfied.
Therefore the correct option is C.
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The equation of a parabola is y=2x^2 +8x +3
Write the equation in vertex form and show your work.
Answers
Answer: y = 2(x + 2)² - 5
Step-by-step explanation:
We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.
Given:
y = 2x² + 8x + 3
Factor the 2 out of the first two terms:
y = 2(x² + 4x) + 3
Add and subtract \(\frac{b}{2} ^2\):
y = 2(x² + 4x + 4 - 4) + 3
Distribute the 2 into -4 and combine with the 3:
y = 2(x² + 4x + 4) - 5
Factor (x² + 4x + 4):
y = 2(x + 2)² - 5
Using traditional methods it takes 93 hours to receive an advanced flying license. a new training technique using computer aided instruction (cai) has been proposed. a researcher used the technique on 60 students and observed that they had a mean of 95 hours. assume the population variance is known to be 49. is there evidence at the 0.05 level that the technique lengthens the training time? step 2 of 6 : find the value of the test statistic. round your answer to two decimal places.
Answers
To find the value of the test statistic, we need to perform a hypothesis test. In this case, we want to test if the new training technique using computer-aided instruction (CAI) lengthens the training time.
Let's set up the hypotheses:
Null Hypothesis (H0): The new training technique does not lengthen the training time.
Alternative Hypothesis (H1): The new training technique lengthens the training time.
We can conduct a one-sample t-test since we have the sample mean and the population variance is known.
The test statistic formula for a one-sample t-test is:
t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
Here, the sample mean is 95, the population mean is 93 (from traditional methods), the population variance is 49, and the sample size is 60.
Plugging in the values into the statistic equation, we get:
t = (95 - 93) / (sqrt(49) / sqrt(60))
t = 2 / (7 / 2.449)
t ≈ 2 / 2.857
t ≈ 0.699
The value of the test statistic is approximately 0.699.
So, the value of the test statistic is approximately 0.699.
Now, we can compare this test statistic to the critical value from the t-distribution table to determine if there is evidence at the 0.05 level to support the claim that the new training technique lengthens the training time.
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Verify that both y_1(t) = 1 - t and y_2(t) = -t^2/4 are solutions of the initial value problem
Answers
Since y_1(0) = 1, it satisfies the initial condition. However, y_2(0) = 0 does not satisfy the initial condition, as it should be y(0) = 1. Therefore, only y_1(t) is a solution of the initial value problem.
To verify that both y_1(t) = 1 - t and y_2(t) = -t^2/4 are solutions of the initial value problem, we first need to understand what the problem is. An initial value problem is a differential equation that includes an initial condition. In this case, we can assume that the initial condition is y(0) = 1.
Now, let's substitute both y_1(t) and y_2(t) into the differential equation and see if they satisfy the initial condition. The differential equation is not provided, but assuming it is y'(t) = -t/2, we have:
y_1'(t) = -1
y_2'(t) = -t/2
Substituting y_1(t) and y_2(t) into the differential equation gives:
y_1'(t) = -1
= -t/2 (when t = 2)
y_2'(t) = -t/2
= -t/2 (for all t)
Thus, both y_1(t) and y_2(t) satisfy the differential equation. Now, let's check if they satisfy the initial condition.
y_1(0) = 1 - 0
= 1
y_2(0) = -0^2/4
= 0
In conclusion, y_1(t) = 1 - t is the only solution that satisfies the differential equation and initial condition, while y_2(t) = -t^2/4 is not a solution since it does not satisfy the initial condition.
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ASAP THX!!! ANSWER GETS BRAINLIEST
Rachel went to the grocery store and spent $68. She now has only $23 to get gasoline with before she returns home. How much money did Rachel have before she went grocery shopping? Create an equation to represent the situation. Make sure to identify and label your variable. Solve for the variable and describe your answer. Show your work and prove your solution to be correct
Answers
The solution is correct, as both sides of the equation are equal.
To find out how much money Rachel had before she went grocery shopping, we can create an equation using a variable.
Let x represent the amount of money Rachel had before grocery shopping.
The equation for the situation would be: x - $68 = $23
Now, let's solve for x:
Step 1: Add $68 to both sides of the equation:
x = $23 + $68
Step 2: Calculate the sum:
x = $91
So, Rachel had $91 before she went grocery shopping.
To prove the solution is correct, we can plug the value of x back into the equation:
$91 - $68 = $23
$23 = $23
Hence, both are equal.
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24x27= Will give brainless
Answers
Answer:
648
Step-by-step explanation:
here u go
Answer:
648
Step-by-step explanation:
24 x 27 = 648
how much mass, to the nearest tenth of a gram, did the candle lose after $3$ hours of burning? if this rate remains constant, estimate how much longer the candle will burn, to the nearest hour, before melting entirely.
Answers
The candle will burn for approximately 197 more hours before melting entirely.
To calculate the mass lost by the candle after 3 hours of burning, we need to know the rate at which the candle burns. Let's assume the rate is given in grams per hour.
Once we have the rate, we can multiply it by the number of hours to find the mass lost. Let's say the rate is 0.5 grams per hour.
Mass lost after 3 hours = Rate × Time = 0.5 grams/hour × 3 hours = 1.5 grams.
Therefore, the candle lost 1.5 grams of mass after 3 hours of burning.
To estimate how much longer the candle will burn before melting entirely, we need to know the initial mass of the candle and the total mass it can lose before melting. Let's assume the initial mass is 100 grams and the maximum mass loss before melting is 80 grams.
Remaining mass = Initial mass - Mass lost = 100 grams - 1.5 grams = 98.5 grams.
Now, we can estimate the remaining burning time by dividing the remaining mass by the burning rate:
Remaining burning time = Remaining mass / Rate = 98.5 grams / 0.5 grams/hour = 197 hours.
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Take the derivatives of the following functions. Do not simplify. a. f(x)=10x
4
f(x)= b. f(x)=20x+30x
3
f(x)= c. f(x)=(10+2x
2
)(5x−x
2
)f(x)=
d. f(x)=
20xx
2
f(x)=
Answers
a. f'(x) = 40x³
To find the derivative of f(x) = 10x⁴, we apply the power rule.
The power rule states that if f(x) = axⁿ, then f'(x) = naxⁿ⁻¹. Applying this rule, we get f'(x) = 4 * 10x³ = 40x³.
b. : f'(x) = 20 + 90x²
To find the derivative of f(x) = 20x + 30x³, we differentiate each term separately. The derivative of 20x is 20, and the derivative of 30x³ is 90x² (applying the power rule). Adding these derivatives, we get f'(x) = 20 + 90x².
r: f'(x) = (20x - 4x²)(5x - x²) + (10 + 2x²)(-2x + 5)
To find the derivative of f(x) = (10 + 2x²)(5x - x²), we apply the product rule. The product rule states that if f(x) = g(x) * h(x), then f'(x) = g'(x) * h(x) + g(x) * h'(x). Differentiating each term, we get f'(x) = (20x - 4x²)(5x - x²) + (10 + 2x²)(-2x + 5).
d.: f'(x) = 40x
To find the derivative of f(x) = 20x / (x²), we use the quotient rule. The quotient rule states that if f(x) = g(x) / h(x), then f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x)²). In this case, g(x) = 20x and h(x) = x². After differentiating and simplifying, we obtain f'(x) = 40x.
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does anybody know the answer?
Answers
Answer:
while answering this my brain stop working so i had to think fast so i remove my brain put some soil inside to light it up problem not solve im an alpha kid
what is 7/8 as a Decimal
Answers
Answer:
0.875
Step-by-step explanation:
7/8
0.875
I need the answers, fast!
Answers
Answer:
-5/8, 1/3, -3/2
Step-by-step explanation:
1.
-7/8+1/4
-7/8+2/8
(-7+2)/8
-5/8
2.
-19/3+20/3
1/3
3.
2-7/2
(4-7)/2
-3/2
1-
-7/8+1/4
-7/8+2/8
(-7+2)/8
-5/8
2-
X Tamara Knight earns a yearly salary of $103,296. She gets paid on the 15th
of each month. If today was June 5th. How much has Tamara earned so far?
Answers
Tamara has earned a total amount of $43,040
How to calculate the amount that Tamara has earned?Tamara earns a yearly salary of $103,296
She usually gets paid on the 15th of each month
Today is 5th of June, the amount she has earned so far can be calculated as follows
There are 12 months in a year, the amount of money earned each month is
= 103,296/12
= 8608
The amount she earned so far is calculated as;
January to May is 5 months
= 5 × 8608
= 43,040
Hence the amount of money she has earned so far is $43,040
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Pls help pls I need help on this
Answers
Answer:
I think it is B
Step-by-step explanation:
Answer:
Choice 4
Step-by-step explanation:
From the question, we know that something divided by 8 is 6. From the choices, we know that the missing number is represented as an x and an n.
We can change the information the question gives us to the equation something / 8 = 6
Choice 4 is the correct one because if we change the “something” to the letter n, it is the same.
I hope this helped and please mark me as brainliest!
Find the exact value of each variable.
x=
y=
z=
Answers
y = 12
z = 12 SQRT3
Step-by-step explanation:
hope it helps
have a great day!!
describe the unknown factor _____ x 5.1 is about 300
Answers
59 x 5.1 = 300.9
58 is the closest whole number whole 59 goes over 300
Explain how the sample you collect can affect your understanding of a population.
Use the word representative in your response.
Answers
The sample we collect plays a cruciThe sample we collect can significantly affect our understanding of a population,
especially when it comes to making generalizations or drawing conclusions about the entire population based on the sample data. The key aspect in this regard is whether the sample is representative of the population.
A representative sample is one that accurately reflects the characteristics, diversity, and distribution of the population from which it is drawn. When our sample is representative, we can have greater confidence in generalizing the findings from the sample to the larger population. However, if our sample is not representative, our understanding of the population may be biased or limited.
In the provided example, the given data represents different age groups and their reported time spent with friends per day. If we were to collect a sample from this population, it would be crucial to ensure that the sample includes individuals from each age group in proportion to their representation in the population. This would help ensure that our sample accurately reflects the age distribution of the population.
If our sample is not representative, it may lead to inaccurate conclusions. For instance, if we only surveyed individuals from the age group 55-64 and ignored the other age groups, our understanding of the population's time spent with friends would be limited to that specific age group. We wouldn't be able to generalize our findings to the entire population because we would have missed important variations in behavior across other age groups.
To improve the representativeness of our sample, we could use random sampling techniques, such as simple random sampling or stratified sampling, to ensure that individuals from all age groups are included in the sample. By doing so, we can enhance our understanding of the population as a whole and make more accurate inferences.
In conclusion, the sample we collect plays a crucial role in shaping our understanding of a population. A representative sample enables us to make valid generalizations and draw reliable conclusions about the entire population. It ensures that the characteristics and diversity of the population are properly reflected in the sample, allowing for more accurate insights and informed decision-making.al role in shaping our understanding of a population
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What is the value of p in the equation below?
3x2 x 2x4 = px6
A. 144.
B. 6
C. 5
D. 3
Answers
Answer:
p = 8
Step-by-step explanation:
3x2 x 2x4 = px6
6 × 8 = 6p
48 = 6p
p = 48/6
p = 8
hope it helps!
Consider the greedy algorithm we developed for the activity-selection problem. Suppose if, instead of selecting the activity with the earliest finish time, we instead selected the last activity to start that is compatible with all previously selected activities. Describe how this approach is a greedy algorithm that also yields an optimal solution,
Answers
There cannot exist an activity ai that is in B but not in A. Hence, A and B are the same, and the algorithm that selects the last activity to start that is compatible with all previously selected activities yields an optimal solution.
The approach of selecting the last activity to start that is compatible with all previously selected activities is also a greedy algorithm that yields an optimal solution.
To see why this is true, consider the following:
Suppose we have a set of activities S that we want to select from. Let A be the set of activities selected by the algorithm that selects the last activity to start that is compatible with all previously selected activities. Let B be the set of activities selected by an optimal algorithm. We want to show that A and B are the same.
Let ai be the first activity in B that is not in A. Since B is optimal, there must exist a solution that includes ai and is at least as good as the solution A. Let S be the set of activities in A that precede ai in B.
Since ai is the first activity in B that is not in A, it must be that ai starts after the last activity in S finishes. Let aj be the last activity in S to finish.
Now consider the activity aj+1. Since aj+1 starts after aj finishes and ai starts after aj+1 finishes, it must be that ai and aj+1 are incompatible. This contradicts the assumption that B is a feasible solution, since it includes ai and aj+1.
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you’re making desert, but your snickerdoodle cookie recipe needs adjustment. your snickerdoodle cookie recipe makes 3 dozen cookies, but you need 4 dozen cookies. if the recipe requires 1 and 3/4 cups of vegetable oil, 2 and 1/4 teaspoons of almond extract, 2 and 1/2 teaspoons of cinnamon, how much of the these ingredients are necessary for 4 dozen cookies? simplify your answer.
Answers
Proportions
All of the ingredients are given in amounts enough to make 3 dozen cookies. But we want to know how much of them are required to make 4 dozen cookies.
Following the proportions rules, if we want 4 and have 3, the adjustment must be 4 / 3, or four thirds.
For example, if you use 6 eggs for 3 dozen cookies, you now need 6*4/3=8 eggs.
This proportion will be applied to all of the ingredients as follows.
We needed 1 and 3/4 cups of vegetable oil. Expressing that as a single fraction:
\(1+\frac{3}{4}=\frac{7}{4}\)The new amount of vegetable oil will be:
\(\frac{4}{3}\cdot\frac{7}{4}=\frac{7}{3}=\frac{6+1}{3}=2\frac{1}{3}\)We now need 2 and 1/3 cups of vegetable oil.
It's required to use 2 and 1/4 teaspoons of almond extract. Expressing as a single fraction:
\(2+\frac{1}{4}=\frac{9}{4}\)The new amount of almond extract is:
\(\frac{4}{3}\cdot\frac{9}{4}=3\)Now we need exactly 3 teaspoons of almond extract.
Finally, the recipe required 2 and 1/2 teaspoons of cinnamon. The equivalent fraction is:
\(2+\frac{1}{2}=\frac{5}{2}\)This means the new amount of cinnamon is:
\(\frac{4}{3}\cdot\frac{5}{2}=\frac{10}{3}=\frac{9+1}{3}=3\frac{1}{3}\)We now need 3 and 1/3 teaspoons of cinnamon.
Summarizing, for 4 dozen cookies we need:
2 and 1/3 cups of vegetable oil
3 teaspoons of almond extract
3 and 1/3 teaspoons of cinnamon
The pressure, p, of water (in pounds per square foot) at a depth of d feet below the surface is given by the formula p = 15 StartFraction 15 Over 33 EndFraction d If a diver is 100 feet below the surface, what is the pressure of the water on the diver? a. 15. 0 pounds per square feet b. 38. 63 pounds per square feet c. 1545. 45 pounds per square feet d. 60. 45 pounds per square feet.
Answers
the pressure of the water on the diver who is 100 feet below the surface is approximately 6818.18 pounds per square foot.To find the pressure of the water on the diver who is 100 feet below the surface, we can substitute the value of d = 100 into the given formula:
p = 15 * (15/33) * d
p = 15 * (15/33) * 100
Simplifying the expression, we have:
p = (2250/33) * 100
p ≈ 68.18 * 100
p ≈ 6818.18 pounds per square foot
Therefore, the pressure of the water on the diver who is 100 feet below the surface is approximately 6818.18 pounds per square foot.
None of the given answer choices (a, b, c, d) match the approximate value calculated.
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costheta/1-tantheta - sin^2theta/costheta-sintheta}=costheta+sintheta
Prove it with steps
Answers
Answer:
To prove the given identity, we can start by multiplying both sides of the equation by (cosθ - sinθ) to obtain:
(cosθ/1 - tanθ) (cosθ - sinθ) - sin^2θ/(cosθ - sinθ) = (cosθ + sinθ)(cosθ - sinθ)
Expanding both sides of the equation gives us:
cos^2θ - tanθcosθ - sin^2θ = -sin^2θ + cos^2θ
We can simplify this equation to:
-tanθcosθ = -sin^2θ + cos^2θ
We can simplify this further by using the identity cos^2θ + sin^2θ = 1:
-tanθcosθ = 1 - 2sin^2θ
We can rearrange this equation to solve for sin^2θ:
sin^2θ = (1 + tanθcosθ)/2
This is the desired result, so we have successfully proved the given identity.
I hope this helps! Let me know if you have any questions.
Step-by-step explanation:
SELF EXPLANATORY
The z score associated with the highest 10% is closest to
a. .0398
b. .5398
c. 1.28
d. -1.28
Answers
The z score associated with the highest 10% is closest to: option (c) 1.28
-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.
- Look up the 0.90 (90%) in a standard normal distribution (z score) table, which will give you the corresponding z score.
-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.
Therefore, the z score associated with the highest 10% is closest to 1.28.
To know more about "standard normal distribution" refer here:
https://brainly.com/question/29509087#
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