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pishuonlain [190]

1 year ago

10

Alyssa drives 10 miles in 20 minutes. If she drove one hour in total at the same rate, how far did she go? i know the answer but

its not working for me on delta math

1 answer:

Fudgin [204]1 year ago

6 0

Answer:

30 miles

Step-by-step explanation:

20 x 3 is 60 minutes

10 x 3 is 30 miles

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If anyone knows about definite integrals for calculus then please I request help! I

kicyunya [14]

Answer:

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx$

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution.</em>

Set <em>u</em>: $\displaystyle u = 4x^{-2}$
[<em>u</em>] Differentiate [Basic Power Rule, Derivative Properties]: $\displaystyle du = \frac{-8}{x^3} \ dx$
[Bounds] Switch: $\displaystyle \left \{ {{x = 9 ,\ u = 4(9)^{-2} = \frac{4}{81}} \atop {x = 5 ,\ u = 4(5)^{-2} = \frac{4}{25}}} \right.$

<u>Step 3: Integrate Pt. 2</u>

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^9_5 {\frac{-8}{x^3}e^\big{4x^{-2}}} \, dx$
[Integral] U-Substitution: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^{\frac{4}{81}}_{\frac{4}{25}} {e^\big{u}} \, du$
[Integral] Exponential Integration: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}(e^\big{u}) \bigg| \limits^{\frac{4}{81}}_{\frac{4}{25}}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8} \bigg( e^\Big{\frac{4}{81}} - e^\Big{\frac{4}{25}} \bigg)$
Simplify: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

4 0

2 years ago

Which is log x+ 6 log(x+7) written as a single logarithm.

Elina [12.6K]

Answer: option d.

Step-by-step explanation:

To solve this problem you must keep on mind the properties of logarithms:

$log(b)-log(a)=log(\frac{b}{a})\\\\log(b)+log(a)=log(ba)\\\\a*log(b)=log(b)^a$

Therefore, knowing the properties, you can write the expression gven in the problem as shown below:

$5logx+6log(x+7)=logx^5+log(x+7)^6=logx^5(x+7)^6$

Then, the answer is the option d.

4 0

2 years ago

Read 2 more answers

a certain shade of blue is made by mixing 1.5 quarts of blue paint with 5 quarts of white paint. If you need a total of 16.25 ga

natita [175]

Answer:

3.75 of blue mixed with 12.5 of white is the correct answer

Step-by-step explanation:

We know the blue and white paints are a 1.5 : 5 ratio, and if we have a total of 16.25 by 1.5 by 5.

1.5 * 2.5 = 3.75

------------------------

5 * 2.5 = 12.5

SO blue is 3.75 and white is 12.5

7 0

2 years ago

Read 2 more answers

you buy 75 candy bars at a cost of $0.49 each what is the total cost of 75 candy bars? use mental math

avanturin [10]

It took me a second but its $36.75

7 0

3 years ago

Read 2 more answers

I forget how to use fractions, what's 7 times 1/2

bekas [8.4K]

In exact form it is 7/2

In decimal form it is 3.5

In mixed number form it is 3 1/2

5 0

2 years ago