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3 years ago

Break apart the addends to find the sum.33+49

1 answer:

8 0

If you break it up it would be 19

Just add them all as single single numbers, Not double digit ones.

Like this, 3+3+4+9 = 19

Hope that helps, Good luck! (:

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kogti [31]

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5 0

4 years ago

Justin has 3 shelves in his roomEach shelf holds 5 toysIf Justin has 19 toys, how many toys don't fit on the shelves?

Liula [17]

Answer:

Step-by-step explanation:

Justin has 3 shelves and each shelf holds 5 toys.

Just has 19 toys , since each shelf can hold 5 ,

5 x 3 = 15

The three shelves will hold 15 toys.

19 - 15 = 4

4 toys will not fit into the shelves

5 0

3 years ago

Read 2 more answers

Area of the bounded curves y=x^2, y=√(7+x)

N76 [4]

Answer:

$\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 5.74773$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

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

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

U-Substitution

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

Step 1: Define

$\displaystyle \left \{ {{y = x^2} \atop {y = \sqrt{7 + x}}} \right.$

Step 2: Identify

Graph the systems of equations - see attachment.

Top Function: $\displaystyle y = \sqrt{7 + x}$

Bottom Function: $\displaystyle y = x^2$

Bounds of Integration: [-1.529, 1.718]

Step 3: Integrate Pt. 1

Substitute in variables [Area of a Region Formula]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx$
[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - \int\limits^{1.718}_{-1.529} {x^2} \, dx$
[Right Integral] Integration Rule [Reverse Power Rule]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - \frac{x^3}{3} \bigg| \limits^{1.718}_{-1.529}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - 2.88176$

Step 4: Integrate Pt. 2

Identify variables for u-substitution.

Set u: $\displaystyle u = 7 + x$
[u] Basic Power Rule [Derivative Rule - Addition/Subtraction]: $\displaystyle du = dx$
[Limits] Switch: $\displaystyle \left \{ {{x = 1.718 ,\ u = 7 + 1.718 = 8.718} \atop {x = -1.529 ,\ u = 7 - 1.529 = 5.471}} \right.$

Step 5: Integrate Pt. 3

[Integral] U-Substitution: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{8.718}_{5.471} {\sqrt{u}} \, du - 2.88176$
[Integral] Integration Rule [Reverse Power Rule]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = \frac{2x^\Big{\frac{3}{2}}}{3} \bigg| \limits^{8.718}_{5.471} - 2.88176$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 8.62949 - 2.88176$
Simplify: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 5.74773$